Kahlenberge and Gabler had him transferred because they were in on an early plot to undermine or arrest Hitler, and feared he would stumble upon it while investigating the murder of Kupiecka (who was reporting back to the German Gestapo). It just happened to be convenient to Tanz to go along with it since it also took the heat off him. Alternatively, Gabler was legitimately having an affair (the lipstick his wife pointed out lends credence to that) and Kahlenberge alone was in on a plot against Hitler. In that case, Gabler's motive would be to avoid the embarrassment of an exposed marital infidelity while Kahlenberge's would have been to avoid the accidental exposure of the plot he was involved in.
Gabler's Book
Judging from in-movie dialog, Gabler's book about World War II was intended to be a self-exculpatory exercise in further propagating the myth of the "Clean Wehrmacht", which fits his character as an opportunist who tries to seek favor from whichever quarter will grant him the best treatment.
